High-order linearly implicit schemes conserving quadratic invariants
From MaRDI portal
Publication:6106927
DOI10.1016/j.apnum.2023.02.005arXiv2203.00944MaRDI QIDQ6106927
Shun Sato, John C. Butcher, Yuto Miyatake
Publication date: 3 July 2023
Published in: Applied Numerical Mathematics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2203.00944
ordinary differential equationsquadratic invariantsgeometric numerical integrationlinearly implicit schemescanonical Runge-Kutta methods
Numerical methods for ordinary differential equations (65Lxx) Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems (65Mxx) Partial differential equations of mathematical physics and other areas of application (35Qxx)
Related Items
Cites Work
- Unnamed Item
- A derivation of energy-preserving exponentially-fitted integrators for Poisson systems
- Linear energy-preserving integrators for Poisson systems
- Linearly first- and second-order, unconditionally energy stable schemes for the phase field crystal model
- The scalar auxiliary variable (SAV) approach for gradient flows
- Numerical simulation of nonlinear Schrödinger systems: A new conservative scheme
- Finite difference schemes for \(\frac{\partial u}{\partial t}=(\frac{\partial}{\partial x})^\alpha\frac{\delta G}{\delta u}\) that inherit energy conservation or dissipation property
- Arbitrarily high-order linear energy stable schemes for gradient flow models
- Novel high-order energy-preserving diagonally implicit Runge-Kutta schemes for nonlinear Hamiltonian ODEs
- Geometric exponential integrators
- Preserving energy resp. dissipation in numerical PDEs using the ``Average Vector Field method
- Time integration and discrete Hamiltonian systems
- Stability of Runge-Kutta Methods for Trajectory Problems
- Discrete Variational Derivative Method
- Geometric Numerical Integration
- A General Framework for Deriving Integral Preserving Numerical Methods for PDEs
- Solving Ordinary Differential Equations I
- Geometric integration using discrete gradients
- Unified Approach to Hamiltonian Systems, Poisson Systems, Gradient Systems, and Systems with Lyapunov Functions or First Integrals
- A Relaxation Scheme for the Nonlinear Schrödinger Equation
- Interpolants for Runge-Kutta formulas
- A Practical Guide to Pseudospectral Methods
- Energy-Decaying Extrapolated RK--SAV Methods for the Allen--Cahn and Cahn--Hilliard Equations
- B-Series
- Dissipative or conservative finite-difference schemes for complex-valued nonlinear partial differential equations
